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hw2 - Hint calculate the true area of cables when the...

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ME 363 Homework No. 2 Name Due: 9/16/2010 1. The recording shown in Table 1 was made during a compression test of a steel cylinder of diameter 15.00 mm and height 22.5 mm, made of hot-rolled AISI 1020 steel. Force P readings at six points are given below together with the instantaneous heights h. Calculate the true stress σ . compressive strain e c and true stain ε . And plot the stress-strain curves. The volume of the specimen is (15.0 2 π /4)(22.5)=3976 mm 3 . Table 1 0 22.5 . . . 177 . . . . . . . . . 1 20.5 115 194 593 8.9 0.09 2 17.5 158 227 695 22.2 0.25 3 14.5 200 274 4 12.5 235 318 5 10.5 290 379 6 8.5 370 468 Point no. h,mm P,kN,A A, mm 2 σ , MPa e c ε 2. A cable is made of two strands of different materials, A and B, and cross sections are as follows: For material A: K=70,000 psi, n=0.5, A 0 = 0.6 in 2 For material B: K=25,000 psi, n=0.5, A 0 = 0.3 in 2 Calculate the maximum tensile force that this cable can withstand prior to necking. Let the value of n be numerically equal to the strain at which necking begins.
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Unformatted text preview: Hint) calculate the true area of cables when the necking occurs. 3. From a tensile test, the stress-strain relationship for material A was obtained as shown in Fig. 1. In the elastic region, the stress is linearly proportional to the stress and represented by σ = E ε with E=30,000,000 psi (207 GPa). Beyond the yield point, the material shows plastic deformation according to σ = K ε n Assuming that ε y =0.02, ε u =0.2, ε f =0.3, K=145,000 psi (1 GPa) and n=0.2, a) calculate toughness. b) calculate the modulus of resilience and estimate the hardness in Brinell and Rockwell C. 4. A bar 0.5 m long is stretched to the strain of 0.15 and then stress relieved. The yield stress of this material is 600 MPa and E=200 GPa. The plastic deformation is described by the strain hardening equation σ = K ε n with K=760 MPa and n=0.2. Determine the length of the bar after the external stress is relieved....
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